Multiple-Constraint-Based Calibration Approach for Cumulative Distribution Function Estimation
Abstract
This paper presents a novel calibration framework for estimating cumulative distribution functions (CDFs) within the context of stratified sampling (StRS) by utilizing multiple calibration constraints and Lata’s distance function. Traditional CDF estimators often neglect the incorporation of auxiliary information, resulting in inefficiencies and biased estimates, particularly for heterogeneous populations. To address this limitation, we propose a new class of CDF estimators that extends existing calibration methodologies by incorporating multiple constraint conditions, thereby enhancing precision and reducing estimation error. Methodological advancement lies in the strategic integration of additional auxiliary information through a generalized calibration mechanism tailored to the structural characteristics of stratified sampling design. This generalization represents a significant extension of the calibration theory into the domain of CDF estimation, an area that remains relatively underexplored in the survey sampling literature. The performance of the proposed estimators was assessed via a comprehensive simulation study involving two real-world datasets: COVID-19 incidence data and apple yield statistics from the agricultural sector. Across both applications, the proposed estimators consistently outperform benchmark estimators in terms of mean squared error (MSE) and precision relative efficiency (PRE) across a range of quantiles.
These findings underscore the practical utility and theoretical relevance of the proposed approach in complex survey environments marked by population heterogeneity. The new estimator family provides a robust and flexible tool for improving the accuracy of CDF estimation in applied survey statistics.
Keywords: CDF; StRS; Calibration Approach; Simulation Study; Relative Efficiency.
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